In researching theories of the brain, certain operational fundamentals, such as memory registration and recall, associative memory, and pattern recognition, suggest much greater complexity than what the basic underlying physical structure provides. For example, a human brain can store more information than would be expected given the number of synapses in the human brain. Therefore, human brain memory is more than just synaptic memory. Other factors come into play in conjunction with the synapses to store all of the information. Since the brain operates in an autonomous asynchronous environment, one theory is that time delays may be important.
For example, if two neurons fire at a common post synaptic target, their spikes travel along axons to the target, and if their spikes arrive simultaneously at the target, a stronger response may be evoked than if their spikes arrive separately. However, axons have propagation velocities that introduce conduction delays; therefore, both the distances from the neurons to the target and the firing times of the neuron spikes determine when the spikes arrive at their target. The propagation velocity may be about one millimeter per millisecond for myelinated fibers and about one-hundred micrometers per millisecond for non-myelinated fibers. Specifically, if a conduction path from a first neuron to the target is about ten millimeters long and a conduction path from a second neuron to the target is about two millimeters long, the first neuron will have to fire about eight milliseconds before the second neuron fires in order for both spikes to arrive simultaneously.
In general, neurons in spiking networks with conduction delays may fire with certain time-locked asynchronous patterns so that their spikes may arrive at targets simultaneously. The additional dimension of time delays in a brain may significantly increase a brain's capacity to represent and process information. Such an activity may be called polychrony. Polychrony may be derived from poly, meaning many, and chronos, meaning time or clock. With an appropriate type of spike-timing dependent synaptic plasticity, spiking networks may self-organize and generate such polychronous activity, which may have relevance to memory, binding and gamma rhythms, mechanisms of attention, pattern recognition, and the like. Polychronous activity in the brain depends on specificity of synaptic connections, geometry and dimensions of axonal fibers, activity-dependent propagation velocities, dynamics of various neurotransmitters, spike-generation mechanisms of neurons, and other biological factors.
Applying polychronous techniques to physical systems, electronic systems, or both may significantly increase the capacities, the functionalities, or both of such systems. Such systems may operate at much higher frequencies than a brain, which may operate in a frequency range up to about 100 hertz. For example, networks having time delays can encompass greater functionalities than comparable networks without time delays. A dynamic system having a given number of state variables may be represented by a differential equation that has a solution space of the same dimension as the number of state variables. However, when asynchronous time delays are added to the dynamic system, a differential-delay equation that is representative of the dynamic system with delays has an infinite dimensional solution space. Thus, there may be significant benefits from a polychronous physical or electronic system, such as arithmetical computations.